This invention relates to the field of optical waveguides and dispersion tailoring in such waveguides.
Optical waveguides guide optical signals to propagate along a preferred path or paths. Accordingly, they can be used to carry optical signal information between different locations and thus they form the basis of optical telecommunication networks. The most prevalent type of optical waveguide is an optical fiber based on index guiding. Such fibers include a core region extending along a waveguide axis and a cladding region surrounding the core about the waveguide axis and having a refractive index less than that of the core region. Because of the index-contrast, optical rays propagating substantially along the waveguide axis in the higher-index core can undergo total internal reflection (TIR) from the core-cladding interface. As a result, the optical fiber guides one or more modes of electromagnetic (EM) radiation to propagate in the core along the waveguide axis. The number of such guided modes increases with core diameter. Notably, the index-guiding mechanism precludes the presence of any cladding modes lying below the lowest-frequency guided mode. Almost all index-guided optical fibers in use commercially are silica-based in which one or both of the core and cladding are doped with impurities to produce the index contrast and generate the core-cladding interface. For example, commonly used silica optical fibers have indices of about 1.45 and index contrasts of up to about 2-3% for wavelengths in the range of 1.5 microns.
One problem with directing optical signals along an optical waveguide is the presence of chromatic or group-velocity dispersion in that waveguide. Such dispersion is a measure of the degree to which different frequencies of the guided radiation propagate at different speeds (i.e., group velocities) along the waveguide axis. Because any optical pulse includes a range of frequencies, dispersion causes an optical pulse to spread in time as its different frequency components travel at different speeds. With such spreading, neighboring pulses or “bits” in an optical signal may begin to overlap and thereby degrade signal detection. Thus, absent compensation, dispersion over an optical transmission length places an upper limit on the bit-rate or bandwidth of an optical signal.
Chromatic dispersion includes two contributions: material dispersion and waveguide dispersion. Material dispersion comes from the frequency-dependence of the refractive index of the material constituents of the optical waveguide. Waveguide dispersion comes from frequency-dependent changes in the spatial distribution of a guided mode. As the spatial distribution of a guided modes changes, it sample different regions of the waveguide, and therefore “sees” a change in the average index of the waveguide that effectively changes its group velocity. In conventional silica optical fibers, material dispersion and waveguide dispersion cancel each other out at approximately 1310 nm producing a point of zero dispersion. Silica optical fibers have also been modified to move the zero dispersion point to around 1550 nm, which corresponds to a minimum in material absorption for silica.
Unfortunately, while operating at zero dispersion minimizes pulse spreading, it also enhances nonlinear interactions in the optical fiber such four wave mixing (FWM) because different frequencies remain phase-matched over large distances. This is particularly problematic in wavelength-division multiplexing (WDM) systems where multiple signals are carried at different wavelengths in a common optical fiber. In such WDM systems, cross-phase modulation introduces cross talk between the different wavelength channels. To address this problem, WDM systems transmit signals through optical fibers that introduce a sufficient dispersion to minimize FWM, and thereafter transmits the signals through a “dispersion compensating fiber” (DCF), to cancel the original dispersion and minimize pulse spreading in the compensated signal. Important criteria for the dispersion compensating fiber is that it provides a large enough dispersion to compensate for the aggregate dispersion of the transmission fiber, that it compensate for the dispersion at each of the WDM channels, and that it does not introduce too much loss or nonlinear effects. Accordingly, one useful measure of a DCF is the figure of merit (FOM), which is the ratio of the dispersion provided by the DCF, e.g., in units of ps/(nm−km), to the losses introduced by the DCF, e.g., in units of dB/km.
In optical fiber transmission systems, losses in the transmission fiber and the DCF are typically compensated by periodic optical amplification and/or detection and subsequent regeneration of the optical signal. In practice, however, even with DCFs that have a large FOM, there is a limit to the length of optical fiber between such dispersion compensation, amplification, and/or regeneration, because the presence of dispersion may enhance other nonlinear effects such as self phase modulation (SPM) that complicate dispersion compensation.